On 12/31/2018 9:14 AM, John Clark wrote:
On Sat, Dec 29, 2018 at 6:37 PM Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
>>> /It's an example of a geodesic being the longest path (in
interval) between two events in 4-space./
>> I think you meant shortest path, there is no unique longest
path it can be made as long as you like.
/> No, I mean longest path. /
I just typed "define:geodesic" into Google and this is what I got:
/adjective/
1.
1.
Relating to or denoting the shortest possible line between two
points on a sphere or other curved surface.
2.
2. Another term for geodetic.
But you do know that the straightest path between events in Minkowski
spacetime is the longest duration path don't you. The Google definition
seems not to consider mixed signature metrics.
/> The stay-home twin experiences the longest duration between
departure and arrival of the traveling twin. /
Yes. Relativity says everything moves in a geodetic unless a force it
acting on them, and if the traveling twin was moving close to the
speed of light but eventually returned to where he started then a
force must have acted on him.
This is not true in curved spacetime. For example two different orbits
of the Earth, both geodesics, can coincide at a pair of events. They
will measure different proper times between those events (twin paradox)
even though neither experienced any force. Even a twin paradox can be
constructed this way by having the traveling twin's velocity reversed by
the gravity of massive body far from the stay-home twin; which in GR is
not a force.
> The traveling twin measures a shorter interval because he takes a
non-geodesic path.
I agree, a force acted on the traveling twin so he took a non-geodesic
path and experienced a shorter proper time between events than his
brother who was on a geodesic. But in Feynman's example no force was
acting on either clock , both were in a inertial frame or close to one
assuming the clocks were small compared to the distance from the
center of the Earth.
What "Feynman's example"?
Brent
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